The probability that at least 10 students in a random sample of 20 are Business majors is 0.139. The probability that at least 16 students in the sample are not Business majors is 0.147.
a. To find the probability that at least 10 students in a random sample of 20 are Business majors, we can use the binomial distribution with parameters n = 20 and p = 0.3 (the probability of success, i.e. being a Business major). Using a calculator or software, we can find this probability as:
P(X >= 10) = 1 - P(X < 10) = 1 - binomcdf(20, 0.3, 9) = 0.139
b. To find the probability that at least 16 students in the sample are not Business majors, we can use the same approach, but with q = 0.7 (the probability of failure, i.e. not being a Business major):
P(X >= 16) = 1 - P(X < 16) = 1 - binomcdf(20, 0.7, 15) = 0.147
c. To find the probability that exactly 10 students in the sample are Business majors, we can use the binomial probability formula:
P(X = 10) = (20 choose 10) * (0.3)^10 * (0.7)^10 = 0.201
d. To find the probability that exactly 12 students in the sample are not Business majors, we can use a similar formula:
P(X = 12) = (20 choose 12) * (0.7)^12 * (0.3)^8 = 0.200
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Trigonometric Functions
pls help and be sure to show all your work !! the second pic is the graph that needs to be plotted for the first question.
A) Values of y will be 1, 0, -1, 0, 1
B) and C) plot the values as shown in below figure.
Define the term Trigonometric Function?Trigonometric functions are a set of mathematical functions that relate the angles and sides of right triangles.
A) for f(x) = cos x; the values of x-y chart are:
x y = f(x)
0 1
[tex]\frac{\pi }{2}[/tex] 0
[tex]\pi[/tex] -1
[tex]\frac{3\pi }{2}[/tex] 0
[tex]2\pi[/tex] 1
B) the points are plotted as given figure below.
C) Connects the dots to show the graph of y = cos x; sown in figure below please check it.
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(cosθsinθ−sinθcosθ)
How was this matrix derived?
the matrix [cosθ sinθ; -sinθ cosθ] represents the rotation of a vector by an angle θ in the counterclockwise direction.
The matrix you have provided is the 2x2 rotation matrix for rotating a vector in the two-dimensional plane by an angle of θ in the counterclockwise direction.
To understand how this matrix is derived, let's consider a vector v = [x, y] in the two-dimensional plane. We want to rotate this vector by an angle of θ in the counterclockwise direction.
We can represent the vector v as a column matrix [x, y] and then multiply it by a rotation matrix R(θ) to obtain the rotated vector. The rotation matrix R(θ) is defined as follows:
cos(θ) -sin(θ)
sin(θ) cos(θ)
Multiplying the vector v by the rotation matrix R(θ) gives:
[x', y'] = [x, y] * R(θ)
[x', y'] = [x cos(θ) - y sin(θ), x sin(θ) + y cos(θ)]
Thus, the rotated vector v' is given by:
v' = [x', y'] = [x cos(θ) - y sin(θ), x sin(θ) + y cos(θ)]
We can see that the elements of the rotation matrix R(θ) correspond to the cosine and sine of the rotation angle θ. The matrix element in the first row and first column (cosθ) gives the amount of x that is rotated into the x' direction, while the matrix element in the first row and second column (-sinθ) gives the amount of y that is rotated into the x' direction. Similarly, the matrix element in the second row and first column (sinθ) gives the amount of x that is rotated into the y' direction, while the matrix element in the second row and second column (cosθ) gives the amount of y that is rotated into the y' direction.
Thus, the matrix [cosθ sinθ; -sinθ cosθ] represents the rotation of a vector by an angle θ in the counterclockwise direction.
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Find the associated z-score or scores that represent the following standard normal areas(hint use the excel function =NORM.S.INV()
A. Middle 50 percent
B. Lowest 5 percent
C. Middle 90%
Answer all questions please(URGENT
The z-scores that represent the middle 50% of the standard normal distribution are between -0.6745 and 0.6745, the lowest 5% of the standard normal distribution is -1.645, and the 90% of the standard normal distribution is between -1.645 and 1.645.
What is the definition of standard normal variation?The mean and variance of a standard normal distribution are both 0. A z distribution is another name for this.
Yes, here are the z-scores for the given standard normal areas:
A. Middle 50%: The area between the 25th and 75th percentiles corresponds to the middle 50% of the standard normal distribution. Using Excel's NORM.S.INV() function, we can calculate the z-scores that correspond to those percentiles as follows:
-0.6745 is the z-score corresponding to the 25th percentile.
The 75th percentile z-score is 0.6745.
As a result, the z-scores representing the middle 50% of the standard normal distribution range between -0.6745 and 0.6745.
B. Lowest 5%: The area to the left of the 5th percentile corresponds to the lowest 5% of the standard normal distribution. Using Excel's NORM.S.INV() function, we can calculate the z-score that corresponds to that percentile as follows:
The z-score associated with the fifth percentile is -1.645.
As a result, the z-score representing the bottom 5% of the standard normal distribution is -1.645.
C. Middle 90%: The area between the 5th and 95th percentiles corresponds to the middle 90% of the standard normal distribution. Using Excel's NORM.S.INV() function, we can calculate the z-scores that correspond to those percentiles as follows:
The z-score associated with the fifth percentile is -1.645.
The z-score associated with the 95th percentile is 1.645.
As a result, the z-scores representing the middle 90% of the standard normal distribution range between -1.645 and 1.645.
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Find the equation of the tangent through the point (2,-2) to the hyperbola x² + y² = 16
Answer: y = -x
Step-by-step explanation:
The equation of the hyperbola is x² - y² = 16.
Taking the derivative of the equation with respect to x, we get:
2x - 2yy' = 0
y' = x / y
At the point (2,-2), we have x = 2 and y = -2. Thus, the slope of the tangent is:
y' = 2 / (-2) = -1
So, the equation of the tangent through the point (2,-2) is:
y + 2 = -1(x - 2)
y + 2 = -x + 2
y = -x
Given x-intercepts of (-1,0), (6, 0) and point (-2, 2) that lies on the
quadratic graph, which equation below represents the correct quadratic
equation in standard form?
Answer:
y = (-1/3)x^2 - 2x + 5/3
Step-by-step explanation:
To find the quadratic equation that passes through these points, we can start by using the standard form of a quadratic equation:
y = ax^2 + bx + c
We know that the graph passes through the point (-2,2), so we can substitute these values into the equation:
2 = a(-2)^2 + b(-2) + c
Simplifying this equation, we get:
4a - 2b + c = 2
We also know that the graph has x-intercepts at (-1,0) and (6,0). This means that when x = -1 and x = 6, the value of y (i.e., the height of the graph) is 0. We can use these two points to write two more equations:
0 = a(-1)^2 + b(-1) + c
0 = a(6)^2 + b(6) + c
Simplifying these equations, we get:
a - b + c = 0
36a + 6b + c = 0
Now we have a system of three equations:
4a - 2b + c = 2
a - b + c = 0
36a + 6b + c = 0
We can solve for a, b, and c using any method of solving systems of equations. One way is to use substitution:
From the second equation, we get:
c = b - a
Substituting this into the other two equations, we get:
4a - 2b + (b - a) = 2
36a + 6b + (b - a) = 0
Simplifying these equations, we get:
3a - b = 1
35a + 7b = -b
Multiplying the first equation by 7 and adding it to the second equation, we eliminate b:
21a = -7
a = -1/3
Substituting this value of a into the first equation, we can solve for b:
4(-1/3) - 2b + (b - (-1/3)) = 2
-4/3 - b + b + 1/3 = 2
b = -2
Finally, we can use either of the first two equations to solve for c:
c = a - b = (-1/3) - (-2) = 5/3
So the quadratic equation in standard form is:
y = (-1/3)x^2 - 2x + 5/3
Suppose we want to choose 2 letters, without replacement, from the 3 letters A, B, and C.
The numbers of ways in which we can select the letters without replacement are: a. order relevant - 6 ways. b. order not relevant- 3 ways.
What are combinations and permutations?Both permutations and combinations count the number of possible ways to select a particular number of things from a bigger collection of options. The distinction is that whereas combinations ignore the order of the components, permutations do. In other words, combinations don't care about the order in which the elements are selected, but permutations require arranging the components in a certain sequence.
Given that, we want to choose 2 letters, without replacement.
a. When the order is relevant we have the following choices:
3 options for the first letter and 2 options for the second letter, that is:
3 x 2 = 6 ways
b. If the order is not relevant we use combinations:
n C r = n! / (r! (n-r)!)
3 C 2 = 3! / (2! (3-2)!) = 3
Hence, the numbers of ways in which we can select the letters are: a. order relevant - 6 ways. b. order not relevant- 3 ways.
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The complete question is:
There is 32 students in class.8 boys out of 20 wear cap and 8 girls out of 12 wear spectacles find the probability that the student is boy who wears cap or girls who doesn't wear spectacles
Answer:
Boy = 40%
Girl = 66.6%
Step-by-step explanation:
1) Work out probability that student is a boy who wears cap
8 boys out of 20 wears a cap so to find the probability we have to do 8 divided by 20
8 ÷ 20 = 0.40.4 × 100 = 40%2) Work out probability for girls who doesn't wear spectacles
To find the probability of girls who doesn't wear spectacles we have to do 8 divided by 12
8 ÷ 12 = 0.666...(recurring)0.666...(recurring) × 100 = 66.6%Hope this helps, have a lovely day! :)
A home has gone up in value over several
decades and is now worth 1354% of its
original sale price of $23,000. What is the
value now?
Answer:
$31,142
Step-by-step explanation:
To convert a percentage into a decimal, you move the decimal two places to the left. 1354% converted into a decimal is 13.54.
$23,000 * 13.54 = $31,142
Rewrite without absolute value for the given condition: |(square root 2) +3 -5|
Answer: We can simplify the expression inside the absolute value first:
|(sqrt(2) + 3 - 5)|
= |(sqrt(2) - 2)|
Since sqrt(2) > 2, we know that sqrt(2) - 2 is negative. Therefore, we can rewrite the absolute value as a negative:
|sqrt(2) - 2| = -(sqrt(2) - 2)
So the expression without absolute value is:
-(sqrt(2) - 2)
Step-by-step explanation:
Samir's statement shows a previous balance of $5,336.22, a payment of $607, and a
new transaction totaling $186. What is his new balance if his APR is 29.0%? Round
answer to hundredths place if answer does not have a hundredths place this use
zeros so it does. Do not include the units. Be sure to attach work for credit
Your Answer:
Samir's new balance is $5,044.17.
To calculate Samir's new balance, add the previous balance, subtract the payment, add the new transaction, and multiply by the interest rate for one period. The following formula can be used to calculate the interest for a single period:
balance * APR / 12 = interest
where APR stands for annual percentage rate and 12 represents the number of months in a year.
When we apply this formula to Samir's balance and APR, we get:
5336.22 * 0.29 / 12 = 128.95 in interest
As a result, the total new balance is:
5336.22 - 607 + 186 + 128.95 = 5044.17
We get the following when we round to the nearest hundredth:
$5,044.17
As a result, Samir now has a balance of $5,044.17.
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under the normal distribution, if the mean of the distribution of raw scores is equal to 100, then its equivalent z-score is equal to
The equivalent z-score for a raw score of 115 under a normal distribution with a mean of 100 and a standard deviation of 15 is 1.
Under the normal distribution, if the mean of the distribution of raw scores is equal to 100 and the standard deviation is known, we can use the z-score formula to calculate the equivalent z-score for any given raw score.
The z-score formula is given by:
z = (x - μ) / σ
where x is the raw score, μ is the mean of the distribution, σ is the standard deviation of the distribution, and z is the corresponding z-score.
Since the mean of the distribution is 100, we have μ = 100. To calculate the z-score, we need to know the standard deviation of the distribution or have information about the distance of the raw score from the mean in terms of standard deviations.
If we assume that the standard deviation is 15, which is a common value used in educational testing, and the raw score is 115, then the corresponding z-score would be:
z = (115 - 100) / 15 = 1
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how do you simplify 7/8 + 3/4?
Answer:
13/8
Step-by-step explanation:
You first find the lcm of 8 and 4 which is 8
Then make a dividing line (/) with the lcm as the numerator.
After which you start diviing the lcm by each denominator of the two terms, and then multiplying with their numerators:
8/8 x 7 + 8/4 x 3 all over the lcm which is 8
(1 x 7 + 2 x 3)/8
(7 + 6)/8
13/8
Find, correct to four decimal places, the length of the curve of intersection of the cylinder4x^2 + y^2 = 4and the planex + y + z = 6
The length of the curve of intersection, correct to four decimal places, is 27.7128 units.
To find the length of the curve of intersection, we need to first parameterize the curve.
From the equation of the cylinder, we have:
4x² + y² = 4
Dividing both sides by 4, we get:
x²/1 + y²/4 = 1
This is the equation of an ellipse centered at the origin with semi-major axis a=1 and semi-minor axis b=2.
From the equation of the plane, we have:
x + y + z = 6
Solving for z, we get:
z = 6 - x - y
So the equation of the curve of intersection is:
r(t) = <t, 2sin(t), 6-t-2sin(t)>
where 0 <= t <= 2π.
To find the length of the curve, we need to integrate the magnitude of its derivative with respect to t:
L = ∫√(dx/dt)² + (dy/dt)² + (dz/dt)² dt
Taking the derivative of r(t), we get:
r'(t) = <1, 2cos(t), -1-2cos(t)>
So the magnitude of r'(t) is:
|r'(t)| = √(1² + (2cos(t))² + (-1-2cos(t))²) = √(9+9cos(t)²)
Therefore, the length of the curve is:
L = ∫_0⁽²π⁾ √(9+9cos(t)²) dt
This integral can be solved using the substitution u = tan(t/2), which gives:
L = 18∫_0∞ 1/√(1+u²) du
This integral can be evaluated using trig substitution, letting u = tanθ, which gives:
L = 18∫_0⁽π/²⁾ secθ dθ = 18 ln|sec(π/4)+tan(π/4)| = 18 ln(1+√2)
Using a calculator, we get:
L ≈ 27.7128
Therefore, the length of the curve of intersection, correct to four decimal places, is 27.7128 units.
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4^(-x)=1/256
I believe it is x=4, but I need how to work it out pls thxxx
Answer:
x = 4
Step-by-step explanation:
using the rule of exponents
• [tex]a^{-m}[/tex] = [tex]\frac{1}{a^{m} }[/tex] , then
[tex]4^{-x}[/tex] = [tex]\frac{1}{4^{x} }[/tex]
and 256 = [tex]4^{4}[/tex]
then
[tex]\frac{1}{4^{x} }[/tex] = [tex]\frac{1}{4^{4} }[/tex]
so
[tex]4^{x}[/tex] = [tex]4^{4}[/tex]
since bases on both sides are equal, bot 4 then equate exponents
x = 4
You run 3 laps around a rectangular field. The field is 100 meters long and 97 meters wide. How many meters do you run?
10 POINTS NEED HELP ASAP!!!! PLEASE HELP ME FIND THE AREA AND THE PERIMETER!!
The area of the composite shape using the area formula for the different shapes is 460.48ft².
What are composite shapes?The area of composite shapes refers to the space occupied by any composite shape. A composite shape is a shape that is made by connecting a few polygons to form the required shape.
These figures or shapes can be built from a wide range of shapes, such as triangles, squares, quadrilaterals, etc. Divide a composite item into basic forms such a square, triangle, rectangle, or hexagon to get its area.
Now in the question,
First let us find the area of the semi-circle.
Area of semi-circle = πr²/2
= [3.14 × (16/2) ²]/2
= (3.14 × 8²)/2
= 200.96/2
= 100.48ft²
Now coming to the rectangle,
area of the rectangle = l × b
= 20 × 15
= 300ft²
Now for calculating the area of the triangle,
area = 1/2 × b × h
= 1/2 × 12 × 10
= 60ft²
Therefore, the area of the total figure = 100.48 + 300 + 60 = 460.48ft².
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Calculate the following limits?
The answer of the given question based on the limits the answers are as follows, (a) lim f(x) = 1 , (b) lim f(x) = 3 , (c) lim f(x) = 3.
What is Graph?A graph is visual representation of data that shows the relationship between two or more variables. Graphs can be used to display wide variety of information, including numerical data, functions, and networks. The most common types of graphs like line graphs, bar graphs, scatter plots, and pie charts.
Graphs are widely used in many fields, like science, economics, engineering, and social sciences, to help people understand and analyze complex data. They are powerful tool for visualizing trends, patterns, and relationships, and are often used to communicate findings to wider audience.
a) The limit of f(x) as x approaches 2 from the left:
We can see from the graph that as x approaches 2 from the left, f(x) approaches 1. Therefore, we can write:
lim f(x) = 1
x→2-
b) The limit of f(x) as x approaches 2 from the right:
Similarly, as x approaches 2 from the right, f(x) approaches 3. Therefore:
lim f(x) = 3
x→2+
c) The limit of f(x) as x approaches 2:
Since the limit from the left and the limit from the right exist and are equal, we can say that the limit of f(x) as x approaches 2 exists and equals the common value of the left and right limits. Therefore:
lim f(x) = 3
x→2
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HELP!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
Similar shapes are shapes whose lengths are in equivalent ratio. [tex]\Delta ABC[/tex] and [tex]\Delta DE[/tex][tex]F[/tex] are similar because the side lengths of both triangles are in equivalent ratio (refer to attachment)
Step 1: Draw a random triangle [tex]\Delta ABC[/tex]
The lengths of two sides and an angle are:
[tex]AB=10[/tex]
[tex]BC=6[/tex]
[tex]\angle C=90^o[/tex]
Step 2: Draw and measure the length of DE
[tex]DE=15[/tex]
Step 3: Calculate the ratio
The corresponding line segment to DE is line segment AB.
So, the ratio (k) is:
[tex]k=\dfrac{DE}{AB}[/tex]
[tex]k=\dfrac{15}{10}[/tex]
[tex]k=1.5[/tex]
Step 4: Multiply the ratio by the other line segment in step 1
In (1), we have:
[tex]BC=6[/tex]
So:
[tex]EF=k\times BC[/tex]
[tex]EF=1.5\times6[/tex]
[tex]EF=9[/tex]
Step 5: Draw a circle with center F and radius EF
The center of the circle is point F and the radius of the circle is 9 units
Step 6: Draw a ray from the center (i.e. point F) to DE
Refer to the attached image for
Triangle ABCTriangle DEFCircle with center F and radius 9Ray from F to DERead more about angles, triangles and circles at:
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Just need to answer to this geometry question, Its a throw back for me.
As the triangles are similar to each other, using congruent theorem, we get the value of side JK = 63.8.
What are similar triangles?Comparable triangles are those that resemble one another but may not be precisely the same size. Comparable items are those that share the same shape but differ in size.
This shows that when shapes are amplified or demagnified, they superimpose one another. This feature of similar shapes is often known as "similarity".
As per the triangles,
Let JK be = x.
GF/GH = JI/JK
⇒ 11/18 = 36 /x
⇒ x = 36 × 18/11
⇒ x = 63.8.
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what is the range of function m?
The range of the function m is [1, ∞). Thus, B is correct option.
What are a function's range and domain?The dοmain οf a functiοn is the cοllectiοn οf values that can be plugged intο it. This set represents the x values in a functiοn like f. (x). A functiοn's range is the set οf values that the functiοn can take οn. This is the set οf values returned by the functiοn when we enter an x value.
Tο determine the range οf functiοn m, we must first determine the set οf all pοssible functiοn οutput values.
Looking at the function graph, we can see that the lowest point is (3, 1) and the highest point is (∞, ∞).
As a result, the function m has a range of [1, ∞).
We can write: in interval notation:
m ∈ [1, ∞) range.
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1. Solve. 4x+4=4
O 1
0 0
O 3
O
-3
Answer:
x = 0Step-by-step explanation:
4x+4 = 4
Subtract 4 from both sides:-
4x+4-4 = 4-4
4x = 0
Divide both sides by 4:-
4x/4 = 0/4
x = 0
Rewrite without parentheses.
-6xy²(8y^6-3x^4+4)
Simplify your answer as much as possible.
with step by step please
Answer: Sure! Here's how you can rewrite -6xy²(8y^6-3x^4+4) without parentheses:
Start by distributing the -6xy² to the terms inside the parentheses:
-6xy²(8y^6) - (-6xy²)(3x^4) - (-6xy²)(4)
Simplify each term using the product rule of exponents:
-48x y^8 + 18x^5 y^2 + 24xy²
So the final answer, without parentheses and simplified, is:
-48x y^8 + 18x^5 y^2 + 24xy²
Enjoy!
Step-by-step explanation:
Desmond makes online purchase of R395 from Lineup store . he gets 46 and half % discount due to loyality points. calculate the amount of discount Desmond receive
Desmοnd receives a discοunt οf R183.675. We can rοund this tο R183.18 οr R183.18, depending οn the desired level οf precisiοn.
What is discοunt?We all are eager abοut availing discοunts, but we barely knοw hοw we get these discοunts. There is a prοper way tο calculate discοunt and that we dο by using a discοunt fοrmula. The discοunt rate fοrmula can either be extracted by subtracting the selling price οf the prοduct frοm its marked price οr by multiplying the discοunt rate οffered and the marked price οf the prοduct. In terms οf Mathematics, the fοrmula fοr discοunt is represented as belοw,
Accοrding tο given infοrmatiοn,
Tο calculate the discοunt Desmοnd receives, we first need tο find 53.5% οf the οriginal price. We can dο this by multiplying the οriginal price by 0.535:
R395 x 0.535 = R211.325
Sο, Desmοnd pays R211.325 fοr his purchase after the discοunt.
Tο find the amοunt οf discοunt, we need tο subtract the discοunted price frοm the οriginal price:
R395 - R211.325 = R183.675
Therefοre, Desmοnd receives a discοunt οf R183.675. We can rοund this tο R183.18 οr R183.18, depending οn the desired level οf precisiοn.
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the simplest form of the expression sqr3-sqr6/sqr3+sqr6?
Answer:
1 - [tex]\frac{2\sqrt{2} }{3}[/tex]
Step-by-step explanation:
[tex]\frac{\sqrt{3}-\sqrt{6} }{\sqrt{3}+\sqrt{6} }[/tex]
rationalise the denominator by multiplying the numerator and denominator by the conjugate of the denominator.
the conjugate of [tex]\sqrt{3}[/tex] + [tex]\sqrt{6}[/tex] is [tex]\sqrt{3}[/tex] - [tex]\sqrt{6}[/tex]
= [tex]\frac{(\sqrt{3}-\sqrt{6})(\sqrt{3}-\sqrt{6}) }{(\sqrt{3}+\sqrt{6})(\sqrt{3}-\sqrt{6}) }[/tex] ← expand numerator/ denominator using FOIL
= [tex]\frac{3-\sqrt{18}-\sqrt{18}+6 }{3-\sqrt{18}+\sqrt{18}+6 }[/tex]
= [tex]\frac{9-2\sqrt{18} }{3+6}[/tex]
= [tex]\frac{9-2(3\sqrt{2}) }{9}[/tex]
= [tex]\frac{9-6\sqrt{2} }{9}[/tex]
= [tex]\frac{9}{9}[/tex] - [tex]\frac{6\sqrt{2} }{9}[/tex]
= 1 - [tex]\frac{2\sqrt{2} }{3}[/tex]
TRUE/FALSE. When calculating probabilities, combinations and permutations are used to find the number of outcomes in a sample space.
TRUE. Combinations and permutations are used in probability calculations to determine the number of possible outcomes in a sample space.
When calculating probabilities, combinations and permutations are used to find the number of outcomes in a sample space. Why?When order is important, permutations are utilized, and when order is not important, combinations are used. The formula P(n,r) = n!/(n-r)!, where n! signifies the factorial of n, and the expression C(n,r) = n!/r!(n-r)!, give the number of permutations of n items taken r at a time and the number of combinations of n objects taken r at a time, respectively.
It is possible to count the number of ways that a subset of items can be chosen from a larger set using both permutations and combinations. These ideas are crucial for estimating probabilities because they let us know how many different outcomes could satisfy a certain condition.
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A company's website states their oven temperatures
display may vary up to 35 degrees higher or lower than the temperature being
produced. Based on this statement, which of the following can represent an
oven's actual temperature, t, if it is displaying a temperature of 350 degrees?
x + 350 = 35
x - 350 =35
x + 35 = 350
x-35 = 350
x≤ 315 and x ≥ 385
315 ≤ x ≤ 385
-∞0 ≤x≤ ∞0
Answer:
The correct answer is:
315 ≤ t ≤ 385
This is because the oven temperature display can vary up to 35 degrees higher or lower than the actual temperature being produced. Therefore, the actual temperature (t) could be 35 degrees higher or lower than the displayed temperature (350 degrees), resulting in a range of possible temperatures from 315 to 385 degrees.
Find the surface area of the figure on the right.
The fig's right side of total surface = 42yds.
What is surface area?
A solid object's surface area is a measurement of the total area that the surface of the object takes up.
The definition of arc length for one-dimensional curves and the definition of surface area for polyhedra (i.e., objects with flat polygonal faces), where the surface area is the sum of the areas of its faces, are both much simpler mathematical concepts than the definition of surface area when there are curved surfaces.
A smooth surface's surface area is determined using its representation as a parametric surface, such as a sphere.
This definition of surface area uses partial derivatives and double integration and is based on techniques used in infinitesimal calculus.
Henri Lebesgue and Hermann Minkowski at the turn of the century sought a general definition of surface area.
According to our question-
(17+17+8)yds
42yds
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let z be a standard normal random variable. find the values of a such that p({z > 1.35}) or {z > 2.34})
The values of a such that p({z > 1.35}) or {z > 2.34}) is 0.0981.
Let z be a standard normal random variable.
The standard normal distribution is a probability distribution that is symmetric around a mean of zero and has a standard deviation of one. It is also referred to as the Gaussian distribution or the normal distribution. This distribution is commonly used in the field of statistics to measure the likelihood of certain outcomes.
We have to determine the values of a such that p({z > 1.35}) or {z > 2.34}).
p(z > 1.35) + p(z > 2.34) = p(z > a)
After using the standard normal distribution table.
0.0885 + 0.0096 = p(z > a)
p(z > a) = 0.0981
p(z > 1.29) = 0.0981
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(c)yz dx + xz dy + xy dz, where c consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1) (d) x2 dx-xy dy + dz, where c is the parabola z = x2, y = 0 from (-1, 0, 1) to (1, 0, 1)
The value of the line integral is 1/2.
To evaluate this line integral, we need to parameterize the curve C that consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1).
Let's parameterize the first segment from (1,0,0) to (0,1,0) using t as the parameter
r(t) = (1-t) * <1,0,0> + t * <0,1,0>
= <1-t, t, 0>
where 0 ≤ t ≤ 1.
Now, let's parameterize the second segment from (0,1,0) to (0,0,1) using s as the parameter
r(s) = (1-s) * <0,1,0> + s * <0,0,1>
= <0, 1-s, s>
where 0 ≤ s ≤ 1.
We can then use the parameterization of C to evaluate the line integral:
∫_c yz dx + xz dy + xy dz
= ∫_0^1 yz dx/dt dt + xz dy/dt dt + xy dz/ds ds
= ∫_0^1 (t(1-t)) 0 dt + ((1-t)t) 0 dt + ((1-t)t) ds
= ∫_0^1 (1-t)t ds
= 1/2
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The given question is incomplete, the complete question is:
∫_c yz dx + xz dy + xy dz, where c consists of straight-line segments joining (1, 0, 0) to (0, 1, 0) to (0, 0, 1) Evaluate Line Integrals
find a parameterization of each of the following surfaces, in terms of sines, cosines, and hyperbolic sines and cosines
Parameterizing a surface over a rectangle Parameterizing the surface z = x²+2y² over the rectangular region R defined by -3 ≤ x ≤ 3, −1 ≤ y ≤ 1 are falls under the range of R.
Let's start by expressing x and y as functions of u and v. Since x varies between -3 and 3 over R, we can use the following parameterization for x:
x = u
where u varies between -3 and 3. Similarly, since y varies between -1 and 1 over R, we can use the following parameterization for y:
y = v
where v varies between -1 and 1.
Next, we can use these parameterizations for x and y to express z as a function of u and v. Substituting x = u and y = v into the equation z = x² + 2y², we get:
z = u² + 2v²
So, the parameterization of the surface z = x² + 2y² over the rectangular region R is given by:
x = u, y = v, z = u² + 2v²
where -3 ≤ u ≤ 3 and -1 ≤ v ≤ 1.
The parameterization allows us to study various properties of the surface z = x² + 2y² over the rectangular region R.
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Complete Question:
Parameterizing a surface over a rectangle Parameterizing the surface z = x²+2y² over the rectangular region R defined by -3 ≤ x ≤ 3, −1 ≤ y ≤ 1.